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Quadratic Spline InterpolationPart 1 of 2
http://numericalmethods.eng.usf.edu
Quadratic Spline ExampleThe upward velocity of a rocket is given as a function of time. Using quadratic splines Find the velocity at t=16 seconds Find the acceleration at t=16 seconds Find the distance covered between t=11 and t=16 seconds
tv(t)sm/s0010227.0415362.7820517.3522.5602.9730901.67
Data and Plot
tv(t)sm/s0010227.0415362.7820517.3522.5602.9730901.67
SolutionLet us set up the equations
Each Spline Goes Through Two Consecutive Data Points
Each Spline Goes Through Two Consecutive Data Points
tv(t)sm/s0010227.0415362.7820517.3522.5602.9730901.67
Derivatives are Continuous at Interior Data Points
Derivatives are continuous at Interior Data PointsAt t=10At t=15At t=20At t=22.5
Last Equation
Final Set of Equations
Coefficients of Spline
iaibici1022.704020.88884.92888.883-0.135635.66-141.6141.6048-33.956554.5550.2088928.86-152.13
END
http://numericalmethods.eng.usf.edu
Quadratic Spline InterpolationPart 2 of 2
http://numericalmethods.eng.usf.edu
Final Solution
Velocity at a Particular Pointa) Velocity at t=16
Acceleration from Velocity Profileb) Acceleration at t=16
Acceleration from Velocity ProfileThe quadratic spline valid at t=16 is given by,
Distance from Velocity Profilec) Find the distance covered by the rocket from t=11s to t=16s.
Distance from Velocity Profile
END
http://numericalmethods.eng.usf.edu
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